Skip to main content
SpringerLink
Log in
Book cover

Expertise in Mathematics Instruction pp 63–84Cite as

Coordinating Characterizations of High Quality Mathematics Teaching: Probing the Intersection

  • Chapter
  • First Online:

Abstract

We present an analysis that probed empirically the relationship among three different views of exceptional mathematics teaching: (a) the operational definition of “highly accomplished teaching” of mathematics used by the National Board for Professional Teaching Standards (NBPTS) in the United States, (b) the effective use of cognitively demanding tasks in the mathematics classroom, and (c) the use of innovative pedagogical strategies. We analyzed samples of instructional practice—lesson artifacts and teachers’ commentaries on lessons—submitted by candidates seeking NBPTS certification in the area of Early Adolescence/Mathematics. The instructional samples were systematically probed for evidence of mathematical and pedagogical features associated with the views of cognitive demand and innovative pedagogy, and the features found in the submissions of applicants who were awarded NBPTS certification are contrasted with those who were not awarded certification. Our analyses detected a fairly strong interaction between the NBPTS view of accomplished teaching and the view of effective mathematics instruction associated with cognitively demanding tasks. Nevertheless, even in these lessons that teachers selected for display as “best practice” examples of their mathematics teaching, innovative pedagogical approaches were not systematically used in ways that supported students’ engagement with cognitively demanding mathematical tasks.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    This chapter extends another analysis of the same data set that has been reported in Silver, Mesa, Morris, Star, and Benken (2009). In that chapter we reported an analysis of mathematical and pedagogical features of submitted portfolio entries, but we did not distinguish between teachers on the basis of NBPTS certification status. In addition, the purpose of the earlier analysis was different from the intent in this chapter.

  2. 2.

    Further details regarding the characteristics of our sample with respect to the total population of applicants seeking NBPTS certification in 1998–1999 are given in Silver et al. (2009).

  3. 3.

    We provide here a summary of key points regarding our data analysis methods. Additional information can be found in Silver et al. (2009).

  4. 4.

    Our usage agreement governing the NBPTS materials does not allow us to provide verbatim reproductions. The narrative summaries provide the essential aspects of the task that pertain to decisions regarding cognitive demand.

References

  • Boaler, J. (1998). Open and closed mathematics: Student experiences and understandings. Journal for Research in Mathematics Education, 29, 41–62.

    Article  Google Scholar 

  • Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside school. Teachers College Record, 110(3), 608–645.

    Google Scholar 

  • Bond, L., Smith, T. W., Baker, W., & Hattie, J. (2000). The certification system of the National Board for Professional Teaching Standards: A construct and consequential validity study. Greensboro, NC: Center for Educational Research and Evaluation.

    Google Scholar 

  • Borko, H., Stecher, B., & Kuffner, K. (2007). Using artifacts to characterize reform oriented instruction: The scoop notebook and rating guide (CSE Tech. Rep. No. 707). Los Angeles: Center for the Study of Evaluation, National Center for Research on Evaluation, Standards, and Student Testing (CRESST). Retrieved January 23, 2008, from http://www.cse.ucla.edu/products/reports/R707.pdf

  • Bransford, J. D., Brown, A. L., & Cocking, R. R. (1999). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press.

    Google Scholar 

  • Brownell, W. A., & Moser, H. E. (1949). Meaningful vs. mechanical learning: A study in Grade III subtraction. Duke University Research Studies in Education, No. 8. Durham, NC: Duke University Press.

    Google Scholar 

  • Brownell, W. A., & Sims, V. M. (1946). The nature of understanding. In N. B. Henry (Ed.), The measurement of understanding (45th yearbook of the National Society for the Study of Education, Part I) (pp. 27–43). Chicago: University of Chicago Press.

    Google Scholar 

  • Carpenter, T. P., Fennema, E., & Franke, M. (1996). Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction. Elementary School Journal, 97(1), 3–20.

    Article  Google Scholar 

  • Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C. P., & Loef, M. (1989). Using knowledge of children’s mathematical thinking in classroom teaching: An experimental study. American Educational Research Journal, 26, 499–531.

    Google Scholar 

  • Clare, L., & Aschbacher, P. R. (2001). Exploring the technical quality of using assignments and student work as indicators of classroom practice. Educational Assessment, 7, 39–59.

    Article  Google Scholar 

  • Cohen, D. K. (1990). A revolution in one classroom: The case of Mrs. Oublier. Educational Evaluation and Policy Analysis, 12, 327–345.

    Google Scholar 

  • Cohen, D. K., McLaughlin, M., & Talbert, J. (Eds.). (1993). Teaching for understanding: Challenges for policy and practice. San Francisco: Jossey-Bass.

    Google Scholar 

  • Doyle, W. (1983). Academic work. Review of Educational Research, 53(2), 159–199.

    Google Scholar 

  • Fawcett, H. P. (1938). The nature of proof: A description and evaluation of certain procedures used in a senior high school to develop an understanding of the nature of proof. New York, NY: Teachers College, Columbia University.

    Google Scholar 

  • Fennema, E., & Romberg, T. A. (Eds.). (1999). Mathematics classrooms that promote understanding. Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Ferrini-Mundy, J., & Schram, T. (Eds.). (1997). The recognizing and recording reform in mathematics education project: Insights, issues, and implications (JRME Monograph No. 8). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Fuson, K. C., & Briars, D. J. (1990). Using a base-ten blocks learning/teaching approach for first- and second-grade place-value and multidigit addition and subtraction. Journal for Research in Mathematics Education, 21, 180–206.

    Article  Google Scholar 

  • Ginsburg, A., Cooke, G., Leinwand, S., Noell, J., & Pollock, E. (2005). Reassessing U.S. international mathematics performance: New findings from the 2003 TIMSS and PISA. Washington, DC: American Institutes for Research.

    Google Scholar 

  • Good, T. L., Grouws, D. A., & Ebmeier, H. (1983). Active mathematics teaching. New York: Longman.

    Google Scholar 

  • Hakel, M. D., Koenig, J. A., & Elliott, S. W. (2008). Assessing accomplished teaching: Advanced-level certification programs. Washington: National Academy Press.

    Google Scholar 

  • Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65–97). New York: Macmillan.

    Google Scholar 

  • Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., et al. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25(4), 12–21.

    Google Scholar 

  • Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Charlotte, NC: Information Age.

    Google Scholar 

  • Hiebert, J., Stigler, J., Jacobs, J., Givvin, K., Garnier, H., & Smith, M., et al. (2005). Mathematics teaching in the United States today (and tomorrow): Results from the TIMSS 1999 video study. Educational Evaluation and Policy Analysis, 27, 111–132.

    Article  Google Scholar 

  • Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning in second-grade arithmetic. American Educational Research Journal, 30, 393–425.

    Google Scholar 

  • Lemke, M., Sen, A., Pahike, E., Partelow, L., Miller, D., Williams, T., et al. (2004). International outcomes of learning in mathematics literacy and problem solving: PISA 2003 results from the U.S. perspective (NCES 2005-003). U.S. Department of Education. Washington, DC: NCES.

    Google Scholar 

  • Matsumura, L. C., Garnier, H., Pascal, J., & Valdés, R. (2002). Measuring instructional quality in accountability systems: Classroom assignments and student achievement. Educational Assessment, 8, 207–229.

    Article  Google Scholar 

  • Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., & Chrostowski, S. J. (2004). TIMSS 2003 international mathematics report: Findings from the IEA’s trends in international mathematics and science study at the fourth and eighth grades. Chestnut Hill, MA: TIMSS & PIRLS International Study Center.

    Google Scholar 

  • National Board for Professional Teaching Standards. (1998). Middle childhood through early adolescence/mathematics standards. Washington, DC: Author.

    Google Scholar 

  • National Center for Education Statistics [NCES]. (2003). Teaching mathematics in seven countries: Result from the TIMSS video study. Washington, DC: U.S. Department of Education.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • Newmann, F. M., & Associates. (1996). Authentic achievement: Restructuring schools for intellectual quality. San Francisco: Jossey-Bass.

    Google Scholar 

  • Romagnano, L. (1994). Wrestling with change: The dilemmas of teaching real mathematics. Portsmouth, NH: Heinemann.

    Google Scholar 

  • Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of “well-taught” mathematics courses. Educational Psychologist, 23(2), 145–166.

    Article  Google Scholar 

  • Silver, E. A. (2003). Lessons learned from examining mathematics teaching around the world. Education Statistics Quarterly, 5(1), 20–23. Retrieved January 23, 2008, from http://nces.ed.gov/programs/quarterly/Vol_5/5_1/q2_3.asp

  • Silver, E. A., Mesa, V. M., Morris, K. A., Star, J. R., & Benken, B. M. (2009). Teaching mathematics for understanding: An analysis of lessons submitted by teachers seeking NBPTS certification. American Educational Research Journal, 46(2), 501–531. DOI: 10 3102/0002831208326559.

    Article  Google Scholar 

  • Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33, 455–488.

    Google Scholar 

  • Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2(1), 50–80.

    Article  Google Scholar 

  • Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2009). Implementing standards-based mathematics instruction: A casebook for professional development (2nd ed.). New York: Teachers College Press.

    Google Scholar 

  • Stigler, J. W., & Hiebert, J. (1999). The teaching gap. New York: Free Press.

    Google Scholar 

  • Stigler, J. W., & Hiebert, J. (2004). Improving mathematics teaching. Educational Leadership, 61(5), 12–16.

    Google Scholar 

  • Stodolsky, S. S. (1988). The subject matters: Classroom activities in math and social sciences. Chicago: University of Chicago.

    Google Scholar 

  • Tarr, J. E., Reys, R. E., Reys, B. J., Chavez, O., Shih, J., & Osterlind, S. J. (2008). The impact of middle-grades mathematics curricula and the classroom learning environment on student achievement. Journal for Research in Mathematics Education, 39, 247–280.

    Google Scholar 

  • Weiss, I. R., & Pasley, J. P. (2004). What is high quality instruction?. Educational Leadership, 61(5), 24–28.

    Google Scholar 

  • Weiss, I. R., Pasley, J. D., Smith, P. S., Banilower, E. R., & Heck, D. J. (2003). Looking inside the classroom: A study of K-12 mathematics and science education in the United States. Chapel Hill, NC: Horizon Research, Inc.

    Google Scholar 

  • Wilson, S. M., & Floden, R. E. (2001). Hedging bets: Standards-based reform in classrooms. In S. Fuhrman (Ed.), From the capitol to the classroom: Standards-based reform in the States. Onehundredth yearbook of the National Society for the Study of Education (pp. 193–216). Chicago: University of Chicago Press.

    Google Scholar 

Download references

Acknowledgement

This study was supported in part by grant #ESI-0083276 from the National Science Foundation (NSF) to the Educational Testing Service (ETS), under the direction of Gail P. Baxter and Edward A. Silver. The authors are grateful to the National Board for Professional Teaching Standards (NBPTS) for granting access to the portfolio data and to members of the ETS staff, especially Rick Tannenbaum, for facilitating access to the data, used in this investigation. Any opinions expressed herein, however, are those of the authors and do not necessarily reflect the views of the NSF, NBPTS, or ETS. The authors acknowledge the contributions of Babette Benken, Kathy Morris, and Jon Star to the study reported herein, and also thank Angus Mairs, Douglas Corey, and Hala Ghousseini for their assistance with aspects of the data coding.

Author information

Authors and Affiliations

  1. School of Education, University of Michigan, Ann Arbor, MI, 48109, USA

    Edward A. Silver

  2. School of Education, University of Michigan, 3111 SEB 610 East University, Ann Arbor, MI, USA

    Vilma Mesa

Authors
  1. Edward A. Silver
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vilma Mesa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Edward A. Silver .

Editor information

Editors and Affiliations

  1. Dept. Teaching, Learning & Culture, Texas A & M University, College Station, 77843-4232, Texas, USA

    Yeping Li

  2. FB Erziehungswissenschaft, Inst. Didaktik der Mathematik, Universität Hamburg, Von Melle Park 8, Hamburg, 20146, Germany

    Gabriele Kaiser

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Silver, E.A., Mesa, V. (2011). Coordinating Characterizations of High Quality Mathematics Teaching: Probing the Intersection. In: Li, Y., Kaiser, G. (eds) Expertise in Mathematics Instruction. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-7707-6_4

Download citation

Publish with us

Policies and ethics

Search

Navigation